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  • Nilʹpotentni pidnapivgrupy napivgrup peretvorenʹ : diseracija na zdobuttja naukokovogo stupenja kandidata fiziko-matematičnih nauk
    Kudryavtseva, Ganna
    The dissertation "Nilpotent subsemigroups of transformation semigroups" is devoted to the study of nilpotent subsemigroups of the symmetric inverse semigroup ▫${\mathcal{IS}}(M)$▫ and the semigroup ... ▫${\mathcal P}Aut_q(V_n)$▫ of all partial automorphisms of a finite vector space. For the semigroups ▫${\mathcal{IS}}(M)$▫ and ▫${\mathcal P}Aut_q(V_n)$▫ we describe the structure of subsemigroups, which are maximal among nilpotent subsemigroups of a fixed nilpotency degree. We establish isomorphism criterion of maximal nilpotent subsemigroups of the semigroup ▫${\mathcal{IS}}(M)$▫ for the case, when ▫$M$▫ is a countable set. We introduce the notion of linear types of linear orders on the set of lines of a finite vector space, and in its terms we establish an isomorphism criterion for maximal nilpotent subsemigroups of the semigroup ▫${\mathcal P}Aut_q(V_n)$▫. We prove that the group of automorphisms of a maximal nilpotent subsemigroup of the semigroup ▫${\mathcal{IS}}(M)$▫ (where ▫$M$▫ is at most countable) is isomorphic to a semidirect product of direct sums of symmetric groups. For maximal nilpotent subsemigroups of ▫${\mathcal{IS}}(M)$▫, ▫$M$▫ being finite, we investigate the structure of their lattices of ideals and compute some combinatorial characteristics of these lattices. The methods and the results of the dissertation can be applied for the further study of nilpotent subsemigroups of different transformation semigroups.
    Type of material - dissertation
    Publication and manufacture - Kyïv : [G. M. Šafranova], 2000
    Language - ukrainian
    COBISS.SI-ID - 15600217

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FMF, Mathematical Library, Lj. Skladišče-Jadranska 19

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